I have figured out how to solve this problem but I'm not getting the correct answer.
A 1000 L tank loses water so that, after t days, the remaining volume is
v(t) = 1000[1-(t/10)]^2 for 0<t<10.
How rapidly is the water being lost when the tank is half full?
I got the derivative fine. -200(1-(t/10))
I know to solve v(t) = 500 then take the value of t and input it into v'(t)
when solving v(t) = 500 I end up with the answer 10-5sqrt(2) or -5(sqrt(2) - 2)
but to get the correct answer to the question it needs to be 5sqrt2
the correct answer is 100sqrt(2) litres/day
thank you for your help!